In my opinion, when we as Christians pray to any Person of the Trinity, we are praying to them all as the one God. We are also commanded to pray to God in Jesus' name (Ephesians 5:20) and in the power of the Holy Spirit, who intercedes on our behalf (Romans 8:26), thus involving all three Persons in any prayer.
At the same time, I would also say that, since each member of the Trinity is identified in Scripture as being associated with specific attributes or functions (the Father as the ultimate source and sustainer of all creation and being; the Son as the Savior who died on our behalf to make our forgiveness, justification, and salvation possible; and the Holy Spirit as the agent through whom believers are sanctified), that prayers related to those specific areas could be validly directed to the Person with whom each is associated.